Single-segment run of The Price of Persia: The Sands of Time done on February 25 2004 with the Xbox version. Time is 2:05 at the final game save as shown at the end of video. 2:09:56 time includes time for final fight and for a death that the game doesn't include.
PoP is a fun game to speed run, because so much of the game is spent doing impressive-looking stunts. I spent two weeks playing the game through many times, optimizing the path through every room to the best of my ability, and this was the run that resulted. Most of the random elements went my way, and I'm quite pleased with the time. I think 2:03 or 2:04 at the final save would be about my limit, but hey, I've already spent a ridiculous amount of time on the game! ;)
There are no major shortcuts to take in the game, but there are many battles which are optional. Skipping the battles does take quite a lot of luck, however, especially since the enemies can knock you down by teleporting into you. (There are also sections where Farah can lag behind, giving you a very sudden Game Over message) That's all part of the challenge.
Sadly, the run was not death-free. I've been through the game once without dying, but the time was 2:07 at the final save. This was a much smoother run. My single death comes near the end and costs me only a little time; it's quite possible I wouldn't have gotten 2:04 even if I hadn't died. So, while it's a pity to leave a death in, I'm satisfied with this as my final run.